Teaching Second Level Maths

vallo

Just wondering if any of you mathematicians could help me out with some retorts to the typcial "why do we have to learn this, miss?" mantra that so many students come out with in maths class.
It's all very well to play the 'general problems with innumeracy' card using examples like pyramid schemes and other scams, but when it comes down to the niitty gritty of calculus, trig or say the binomial theorem, it is hard to come up with a relevant answer.
Anybody got something better than 'brain exercise'?

Son Goku

vallo wrote:

Just wondering if any of you mathematicians could help me out with some retorts to the typcial "why do we have to learn this, miss?" mantra that so many students come out with in maths class.
It's all very well to play the 'general problems with innumeracy' card using examples like pyramid schemes and other scams, but when it comes down to the niitty gritty of calculus, trig or say the binomial theorem, it is hard to come up with a relevant answer.
Anybody got something better than 'brain exercise'?

I wouldn't suggest saying anything to them.
Leaving Cert mathematics is boring and eventually useless to those who decide to pursue a career in mathematics. To those who don't it is solely useless.

Anytime you say anything about the worth of math, only the students who already think maths is something important will listen.
i.e. You will be preaching to the choir.

This not unique to Maths. For instance only those who already enjoy Irish will like it in secondary school. It is very unlikely that those who don't will be convinced. People only take a liking to subjects they detest in school once they escape the school environment.

ecksor

Maths isn't the worst LC course going. I didn't find it boring anyway.

From the "Useful links" thread I stickied at the top of the forum,

http://plus.maths.org/about.html
http://www.cut-the-knot.org/index.shtml

may be of use.

Tar.Aldarion

I would say what my maths teacher said, you'll find out in university.Took the heat off himself. Somethimes he would give examples, and they were so crazy/interesting people would listen. Ah memories, great teacher.
You don't really have to tell them much.

vallo

My goodness you are a cynical bunch over here on this board, most of you anyway!
I have to disagree with what you say about students either liking or disliking a subject and there being no point in trying to change things. I've taught in loads of schools and I always do a test on students' favourite subjects really to find out who are the popular teachers who foster a love for the subject within their students and who aren't - it also provides data for the students pie charts and bar charts but that is by-the-way ;-)
Anyway, without fail, I find huge numbers in one class loving say History (or even Irish) or Geography while in another class with a different teacher that subject might come bottom in terms of popularity.
Anyway, speaking as people who are good at maths, your experience was probably different from the norm.
Thanks for those links ecksor - i happened accross the cut-the-knot one some time ago but couldn't find it again.
Thanks everyone for the feedback - if you do happen to think of a killer application for some leaving cert maths that might pique the interest of a teenager I'm all ears.

Son Goku

vallo wrote:

My goodness you are a cynical bunch over here on this board, most of you anyway!
I have to disagree with what you say about students either liking or disliking a subject and there being no point in trying to change things. I've taught in loads of schools and I always do a test on students' favourite subjects really to find out who are the popular teachers who foster a love for the subject within their students and who aren't - it also provides data for the students pie charts and bar charts but that is by-the-way ;-)

It's not being cynical. A lot of studies show that maths in school stands out as satisfying a very specific kind of middle ground student.
People who love it get very bored and you can't change that, outside of altering the curriculum and making it too hard.
People who don't have a knack for it will feel they are under pressure, something which I think you can only partially alleviate not remove.

The only people who "trying to change things" will work on, is the studious middle ground student who is indifferent to the subject, but does quite well in exams.

vallo

Son Goku wrote:

It's not being cynical. A lot of studies show that maths in school stands out as satisfying a very specific kind of middle ground student.

That certainly isn't my experience - can you give me some pointers to the "lot of " studies you're referring to?

People who love it get very bored and you can't change that, outside of altering the curriculum and making it too hard.

Ehhhh ... of course you can! More difficult problems, even going off-piste with some forays into 3rd level maths, advanced puzzles + brainteasers ....

People who don't have a knack for it will feel they are under pressure, something which I think you can only partially alleviate not remove.

This is the most rewarding part of teaching maths!

The only people who "trying to change things" will work on, is the studious middle ground student who is indifferent to the subject, but does quite well in exams.

Perhaps by making them slightly less indifferent to the subject?

Anyway, you obviously have a low opinion of the education system for whatever reason. I strongly disagree about the potential for learning that exists. Sure, education is wasted on the young, but unless we decide to restructure society backwards it is up to teachers and the education system to try to improve things.

Thanks anyway for your feedback and I am genuinely interested in reading the research you refer to.

Son Goku

I don't have a low opinion of the education system. I think it's great the depth we study some subjects in.
Particularly history is one of the Leaving Certs very satisfying subjects.

The unfortunate thing is that maths has a very unusual ability spread compared to a lot of other subjects which makes it very difficult to get it right.

Ehhhh ... of course you can! More difficult problems, even going off-piste with some forays into 3rd level maths, advanced puzzles + brainteasers ....

When I was in school this would have been brilliant, I agree.
However, how will you do this and make sure the leaving course is covered for the average student.

I appreciate what you're doing and if you are able to do it I only wish I had you as a second level teacher, but you can appreciate why I would consider this a difficult task at best.

vallo

Son Goku wrote:

but you can appreciate why I would consider this a difficult task at best.

well ... that's why they pay us the big bucks!!

spurious

vallo wrote:

Anybody got something better than 'brain exercise'?

Education.

We'd all be pretty poorly off if the only things we ever experienced and sought to experience were things we would 'use' (directly) in life at some stage.

Señor Juárez

The LC maths course is actually pretty good... and if you intend to go to college at all, most courses are going to encompass something which builds on the LC maths course, or some aspect of it.

SGKM

You could tell them college is where they use it. Almost all college courses use maths to some extent and the relevance of leaving and junior cert maths becomes apparent.

I'm doing a degree in economics and finance,until 1st year I couldnt see the point of half of the maths that I studied for my leaving. Calculus,Integration,Probability,Algebra and Sequences/Series were all part of my 1st year course. A commerce degree would use those same areas of L.C. maths but not to the same extent as we do. Trigonometry and Geometry would be used in other courses like engineering and probably science.

breadmonkey

I too found leaving cert maths interesting to some extent, particularly the differential and integral calculus. I don't see how they could change it. I mean, it's quite broad at the moment and there's no point in thinnnig it out to only get a superficial knowledge (relatively speaking) of a few areas. Just my 2c.

seinstein

you could say because it is the basis for any type of math you will do in the future. calculus for example; in the lc you only sratch the surface of what you will be able to choose in college. and besides, the students will be able to choose themselves what subject they do in college. in relation to this, they will probably find that no matter what subject they decide to do in college, at least some aspect of it will involve the some of the math they learned in the LC.

oRlyYaRly

Just tell them if they want to learn maths that's relevant to "real life", they're more than welcome in the foundation level class.

Nietzschean

Son Goku wrote:

Leaving Cert mathematics is boring and eventually useless to those who decide to pursue a career in mathematics. To those who don't it is solely useless.

That sounds like a terrible misconception, its like saying i shouldn't do any english classes after primary school because i can write it and speak it, sure what else would i be wanting to do?

The most basic of which is that learning maths utilises the brian, giving the brain a work out can't be but a good thing.(e.g. brain training games for nintendo DS t hat are massive sellars...)

If you wanna look at differention, integration and other such things, simply understanding how a car moves when you see it, general rate of changes. fundamental parts of physics and the real world around us are based on these topics, everyone should know them.

Statistics, alot of stats tends to be probabilities and risk analysis, which is a large part of our daily lives, "If i cross the road how likely is it that car will hit me" , while not everyone is really going to do the sums of this on the fly mostly subconciously such practice in risk analysis has the potential to help people notice bad choices before they make them.

Trig, the problem with lc level is unless you do physics or app math not enough applications of this are shown, just forumla's. I think it should be emphasised where this maths comes into real things such as sports, give an introduction few classes to the physics of a few sports before teaching it, i imagine students would respond better if they could see real world applications(angles to do with kicking soccer balls, firing intercontential missiles , etc...)